# Private Blotto: Viewpoint Competition with Polarized Agents

## TL;DR

This paper introduces the Private Blotto game, analyzing how independent agents allocate effort across items with different outcome functions, revealing stability conditions and implications for social media and political competition.

## Contribution

It characterizes the Nash stability of the Private Blotto game and compares the effects of median versus mean outcome functions on effort allocation.

## Key findings

- Stable arrangements are rare for median outcomes with many agents but can have high misallocated effort.
- Unstable arrangements for mean outcomes can occur with many agents, but stable ones have low effort misallocation.
- Implications for social media and political systems are discussed based on the game analysis.

## Abstract

Social media platforms are responsible for collecting and disseminating vast quantities of content. Recently, however, they have also begun enlisting users in helping annotate this content - for example, to provide context or label disinformation. However, users may act strategically, sometimes reflecting biases (e.g. political) about the "right" label. How can social media platforms design their systems to use human time most efficiently? Historically, competition over multiple items has been explored in the Colonel Blotto game setting (Borel, 1921). However, they were originally designed to model two centrally-controlled armies competing over zero-sum "items", a specific scenario with limited modern-day application. In this work, we propose and study the Private Blotto game, a variant with the key difference that individual agents act independently, without being coordinated by a central "Colonel". We completely characterize the Nash stability of this game and how this impacts the amount of "misallocated effort" of users on unimportant items. We show that the outcome function (aggregating multiple labels on a single item) has a critical impact, and specifically contrast a majority rule outcome (the median) as compared to a smoother outcome function (mean). In general, for median outcomes we show that instances without stable arrangements only occur for relatively few numbers of agents, but stable arrangements may have very high levels of misallocated effort. For mean outcome functions, we show that unstable arrangements can occur even for arbitrarily large numbers of agents, but when stable arrangements exist, they always have low misallocated effort. We conclude by discussing implications our results have for motivating examples in social media platforms and political competition.